User contributions for Jp2916

19 November 2018

• 11:4111:41, 19 November 2018 diff hist 0 Rep:Cmpjp2916 →TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. How big a lattice do you think is big enough to capture the long range fluctuations?
• 11:4111:41, 19 November 2018 diff hist +24 Rep:Cmpjp2916 →TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. How big a lattice do you think is big enough to capture the long range fluctuations?
• 11:3911:39, 19 November 2018 diff hist −623 Rep:Cmpjp2916 /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
• 11:3811:38, 19 November 2018 diff hist +610 Rep:Cmpjp2916 /* TASK: How many cycles are typically needed for the system to go from its random starting position to the equilibrium state? Modify your statistics() and montecarlostep() functions so that the first N cycles of the simulation are ignored when calcula...
• 11:2611:26, 19 November 2018 diff hist −500 Rep:Cmpjp2916 /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
• 11:2511:25, 19 November 2018 diff hist +54 Rep:Cmpjp2916 →The Effect of Temperature

18 November 2018

• 14:4614:46, 18 November 2018 diff hist −6 Rep:Cmpjp2916 →Calculating the Heat Capacity
• 14:4514:45, 18 November 2018 diff hist −17 Rep:Cmpjp2916 →one more
• 14:4514:45, 18 November 2018 diff hist −37 Rep:Cmpjp2916 →one more
• 14:4314:43, 18 November 2018 diff hist −134 Rep:Cmpjp2916 →one more
• 14:4314:43, 18 November 2018 diff hist +332 Rep:Cmpjp2916 →Calculating the Heat Capacity
• 14:3614:36, 18 November 2018 diff hist +11 Rep:Cmpjp2916 →one more
• 14:3614:36, 18 November 2018 diff hist −122 Rep:Cmpjp2916 →Calculating the Heat Capacity
• 14:3414:34, 18 November 2018 diff hist −158 Rep:Cmpjp2916 →one more
• 14:2914:29, 18 November 2018 diff hist +7 Rep:Cmpjp2916 →one more
• 14:2914:29, 18 November 2018 diff hist +365 Rep:Cmpjp2916 →Calculating the Heat Capacity
• 14:2514:25, 18 November 2018 diff hist +5 Rep:Cmpjp2916 →one more
• 14:2514:25, 18 November 2018 diff hist +671 Rep:Cmpjp2916 →one more
• 13:3513:35, 18 November 2018 diff hist +152 Rep:Cmpjp2916 →TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section.
• 13:3313:33, 18 November 2018 diff hist 0 N File:Magjp2916.png No edit summary current
• 13:3313:33, 18 November 2018 diff hist +23 Rep:Cmpjp2916 →TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. How big a lattice do you think is big enough to capture the long range fluctuations?
• 13:3013:30, 18 November 2018 diff hist +22 Rep:Cmpjp2916 →TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section.
• 13:3013:30, 18 November 2018 diff hist 0 N File:Hcjp2916.png No edit summary current
• 13:3013:30, 18 November 2018 diff hist −489 Rep:Cmpjp2916 /* TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot show...
• 13:2913:29, 18 November 2018 diff hist +90 Rep:Cmpjp2916 /* TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot show...
• 13:2813:28, 18 November 2018 diff hist 0 N File:Ssjp2916.png No edit summary current
• 13:1413:14, 18 November 2018 diff hist −313 Rep:Cmpjp2916 /* TASK: complete the functions energy() and magnetisation(), which should return the energy of the lattice and the total magnetisation, respectively. In the energy() function you may assume that J=1.0 at all times (in fact, we are working in reduced u...
• 13:0513:05, 18 November 2018 diff hist +960 Rep:Cmpjp2916 →TASK: A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. For each lattice size, plot the C++ data against your data.
• 13:0413:04, 18 November 2018 diff hist 0 N File:Curiejp2916.png No edit summary
• 12:5112:51, 18 November 2018 diff hist +221 Rep:Cmpjp2916 →Locating the Curie Temperature
• 12:5012:50, 18 November 2018 diff hist 0 N File:Compjp2916.png No edit summary current
• 12:2312:23, 18 November 2018 diff hist +56 Rep:Cmpjp2916 →TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section.

17 November 2018

• 16:5116:51, 17 November 2018 diff hist +3 Rep:Cmpjp2916 →TASK: Calculate the magnetisation of the 1D and 2D lattices in figure 1. What magnetisation would you expect to observe for an Ising lattice with D = 3,\ N=1000 at absolute zero?
• 16:5016:50, 17 November 2018 diff hist +429 Rep:Cmpjp2916 →TASK: Calculate the magnetisation of the 1D and 2D lattices in figure 1. What magnetisation would you expect to observe for an Ising lattice with D = 3,\ N=1000 at absolute zero?
• 16:2516:25, 17 November 2018 diff hist +297 Rep:Cmpjp2916 →TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section.
• 16:2316:23, 17 November 2018 diff hist +871 Rep:Cmpjp2916 →Locating the Curie Temperature
• 16:0616:06, 17 November 2018 diff hist +168 Rep:Cmpjp2916 /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
• 16:0616:06, 17 November 2018 diff hist 0 Rep:Cmpjp2916 /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
• 16:0516:05, 17 November 2018 diff hist +586 Rep:Cmpjp2916 /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
• 15:5615:56, 17 November 2018 diff hist 0 N File:Eot32jp2916.png No edit summary current
• 15:5615:56, 17 November 2018 diff hist 0 N File:Eot16jp2916.png No edit summary current
• 15:5615:56, 17 November 2018 diff hist 0 N File:Eot8jp2916.png No edit summary current
• 15:2915:29, 17 November 2018 diff hist +438 Rep:Cmpjp2916 /* TASK: Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the...
• 15:1415:14, 17 November 2018 diff hist +811 Rep:Cmpjp2916 →TASK: Show that the lowest possible energy for the Ising model is E\ =\ -DNJ, where D is the number of dimensions and N is the total number of spins. What is the multiplicity of this state? Calculate its entropy.

14 November 2018

• 14:2214:22, 14 November 2018 diff hist −1,468 Rep:Cmpjp2916 /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
• 14:2114:21, 14 November 2018 diff hist +1,468 Rep:Cmpjp2916 /* TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot show...
• 14:2014:20, 14 November 2018 diff hist +1,468 Rep:Cmpjp2916 /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
• 14:1914:19, 14 November 2018 diff hist +2,847 Rep:Cmpjp2916 /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
• 14:1414:14, 14 November 2018 diff hist +949 Rep:Cmpjp2916 /* TASK: Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy()...
• 14:1114:11, 14 November 2018 diff hist +27 Rep:Cmpjp2916 →TASK: Run the ILcheck.py script from the IPython Qt console using the command